Transonic compressor rotors with non-monotonic meanline angle distributions

ABSTRACT

Airfoils are provided having non-monotonic meanline angle distributions and local negative camber along a length of the meanline between a point on a leading edge of the airfoil and a point on the trailing edge of the airfoil. The improved airfoil shape decreases the peak of a Mach number of a shock wave that develops in a passage between adjacent airfoils and attenuates or eliminates the shock wave at the suction surface of the airfoil within the passage. A blade constructed by this type of airfoil provides improved fluid flow in the passages between the airfoils, increased efficiency and an improved stall margin, among other benefits.

FIELD OF THE INVENTION

This invention is directed generally to axial flow rotary machines having transonic airfoils. More particularly, the invention is directed to combustion turbine engines having transonic compressor rotors or fans with non-monotonic meanline angle distributions.

BACKGROUND

Combustion turbine engines include three main components: a compressor for compressing a fluid, such as air; a combustor for mixing the compressed fluid with fuel and igniting the mixture; and a turbine for producing power. These components are generally configured in series and are sealed to form a gas-tight system.

The compressor, fan and turbine components typically contain many rows of opposing airfoil-shaped blades that are grouped in stages. In the compressor component, the stages typically include a row of rotating blades (rotors) followed by a row of stationary blades (stators), as viewed from a direction of fluid flow from an inlet side to an outlet side. In the turbine component, the stages typically include a row of stationary blades (vanes) followed by a row of rotating blades (blades), as viewed in a direction of fluid flow from an inlet side to an outlet side. The combustor component is located between the compressor component and the turbine component.

The stages within the compressor component and the turbine component are configured in series and each contributes to a pressure rise in the compressor component and a pressure drop in the turbine component. The rotating blade rows are coupled to a shaft that runs through the compressor component to the turbine component. The stationary blade rows are typically coupled to an interior periphery of the corresponding compressor and turbine components.

The compressor component is configured to include a funnel-shaped structure or annulus that reduces a volume available to an air mass that travels from the inlet side to the outlet side. The compressor component receives ambient air at the inlet side. The blades within the compressor component transfer mechanical energy into the flow through aerodynamic lift and force the air mass through the annulus.

As the fluid passes through the stages, fluid molecules closely follow the top and bottom surfaces of the airfoils. As the fluid velocity decreases over the airfoils, the fluid may experience separation from the top and/or bottom surfaces and/or shock waves may develop in the passage ways between the airfoils. Fluid separation from the airfoils and/or shock waves cause aerodynamic losses. The aerodynamic losses limit the efficiency of the airfoils. The aerodynamic losses are of particular concern in transonic environments that contain adjacent regions of subsonic and supersonic local velocities.

While advances have been made in reducing losses in a transonic environment by optimizing the contour of the airfoils, conventional systems have relied on compressor airfoil designs that employ monotonic meanline angle distributions. These conventional systems include several drawbacks. A need remains to develop compressor airfoil designs that include relatively simple shapes and provide improved aerodynamic flow performance in the transonic environment.

SUMMARY OF THE INVENTION

Various aspects of the invention overcome at least some of these and other drawbacks of existing systems. According to one embodiment of the invention, an airfoil is provided in an adverse pressure gradient, wherein the adverse pressure gradient means that pressure increases as the fluid moves downstream, such as from an inlet to an outlet. The airfoil includes a meanline that is defined between a suction surface and a pressure surface. The meanline includes a non-monotonic meanline angle distribution along a length of the meanline between a point on a leading edge and a point on a trailing edge of an airfoil. A thickness distribution is superimposed along the meanline, between a leading edge and a trailing edge of the airfoil, to obtain the airfoil shape defined by the suction surface and the pressure surface.

According to one embodiment of the invention, a high efficiency and high operability (stall margin) gas turbine engine is provided through improved compressor airfoil designs. The airfoil shapes at different span locations are designed to satisfy flow angle turning for the needed work input, as determined by the Euler work equation. The invention provides improved airfoils that more efficiently turn the fluid flow from a tangential (rotation) direction to an axial direction to achieve passage area expansion and flow diffusion.

According to one embodiment, the invention provides improved fluid flow in the passages between airfoils and higher efficiency by providing airfoils that include non-monotonic meanline slope angles for reducing the peak Mach number in the passages. The improved airfoils with the non-monotonic meanline slope angles may also weaken or remove the shock waves.

According to another embodiment, the invention provides improved fluid flow in the passages and higher operability by providing airfoils with non-monotonic meanline slope angles that reduce fluid separation at the airfoil.

According to another embodiment, the invention provides a non-monotonic meanline angle distribution technique with local negative camber applied to a transonic rotor blade from the hub region to the tip region, wherein the negative camber is provided downstream of the throat so as not to reduce mass flow through the rotor section.

These and other embodiments are described in more detail below.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and form a part of the specification, illustrate embodiments of the presently disclosed invention and, together with the description, disclose the principles of the invention.

FIG. 1 illustrates a compressor rotor assembly according to one embodiment of the invention.

FIG. 2 illustrates an airfoil according to one embodiment of the invention.

FIGS. 3A and 3B illustrate meanline angle distribution graphs for monotonic and non-monotonic rotor designs according to one embodiment of the invention.

FIG. 4 illustrates an airfoil configuration having a passage according to one embodiment of the invention.

FIGS. 5A and 5B illustrate flow passage area distribution graphs for monotonic and non-monotonic rotor designs according to one embodiment of the invention.

FIG. 6A illustrates a flow angle vs. span graph for monotonic and non-monotonic rotor designs according to one embodiment of the invention.

FIG. 6B illustrates an absolute total pressure vs. span graph for monotonic and non-monotonic rotor designs according to one embodiment of the invention.

FIGS. 7A and 7B illustrate surface isentropic Mach number graphs for monotonic and non-monotonic rotor designs according to one embodiment of the invention.

FIG. 8 illustrates a normalized efficiency graph for monotonic and non-monotonic rotor designs according to one embodiment of the invention.

FIG. 9( a)-9(f) illustrate Mach number contour graphs for monotonic and non-monotonic rotor designs according to one embodiment of the invention.

DETAILED DESCRIPTION OF THE INVENTION

While specific embodiments of the invention are discussed herein and are illustrated in the drawings appended hereto, the invention encompasses a broader spectrum than the specific subject matter described and illustrated. As would be appreciated by those skilled in the art, the embodiments described herein provide but a few examples of the broad scope of the invention. There is no intention to limit the scope of the invention only to the embodiments described.

According to one embodiment of the invention illustrated in FIG. 1, a compressor rotor assembly 10 is provided for a gas turbine. The compressor rotor assembly 10 includes a rotor hub 12 that rotates about an axis 14. A plurality of rotors 16 extend outwardly from the rotor hub 12. According to one embodiment, the rotors 16 extend in a radial direction away from the rotor hub 12. Fluid 17 flows axially along direction 17 and passes between adjacent rotors 16 at passages 11. The rotors 16 are defined by airfoils 13, wherein the airfoils 13 include a fist side having a convex surface or suction surface 20 and a second surface having a concave surface or pressure surface 22 as illustrated in FIG. 2.

According to one embodiment of the invention illustrated in FIG. 2, the suction surface 20 and the pressure surface 22 of the airfoil 13 are joined together at a leading edge 24 and at a trailing edge 26. A meanline 27 connects a point A on the leading edge 24 and a point B on the trailing edge 26, wherein the meanline 27 is defined between the suction surface 20 and the pressure surface 22 of the airfoil 13. According to one embodiment of the invention, the meanline 27 includes a non-monotonic meanline angle distribution along a length of the meanline 27 between a point on the leading edge 24 and a point on the trailing edge 26 of the airfoil 13.

According to one embodiment of the invention, the airfoil 13 section shape is constructed on an unwrapped surface, which is an flat surface that is unwrapped from a conical stream surface and matches the flow turning that is determined by a circumferential average through flow solution. On the unwrapped surface, the airfoil 13 is determined by specifying the meanline angle distribution, which determines the meanline shape. Thickness distributions are superimposed along the meanline shape to obtain the airfoil shape, wherein the airfoil shape is defined by the suction surface and the pressure surface.

According to one embodiment of the invention, a thickness distribution is defined to be perpendicular to the meanline 27 with equal distance on both sides (T_(s) and T_(p)) of the meanline 27. The suction surface 20 is defined by the points on the upper surface. The pressure surface 22 is defined by the points on the lower surface. According to one embodiment of the invention, the thickness distribution may be symmetric about the meanline 27. According to another embodiment of the invention, a thickness distribution include unequal distances on both sides (T_(s) and T_(p)) of the meanline 27. According to one embodiment of the invention, the thickness distribution may be asymmetric about the meanline 27. The non-monotonic meanline angle distribution may not be visible by the contours of the meanline 27, the suction surface 20 and/or the pressure surface 22 in FIG. 2. The non-monotonic meanline angle distribution is illustrated in FIGS. 3A and 3B, as described in detail below.

According to one embodiment of the invention, the meanline angle distribution determines the area distribution and flow turning, thereby determining the work load distribution along the rotor 16. The rotor geometry may be obtained by stacking the airfoil sections at different conical stream surfaces from the hub portion of the rotor to the tip portion of the rotor along a stacking axis. According to one embodiment, the stacking axis may be the leading edge to enable control of the leading edge sweep. According to another embodiment, the stacking axis may be the center of gravity to match any structural parameters.

According to one embodiment of the invention, the airfoil 13 may be provided in an adverse pressure gradient, wherein the adverse pressure gradient is understood to mean that pressure increases as the fluid moves downstream between adjacent airfoils 13, such as from an inlet to an outlet at passages 11.

According to one embodiment of the invention, the meanline 27 includes a non-monotonic meanline angle distribution or non-consistent slope sign of the meanline angle distribution (e.g., the slope of the meanline angle may increase and/or decrease) along the length of the meanline 27. The meanline angle is defined by the slope angle between a line that is positioned tangent to the meanline 27 and an axial direction along the length of the meanline 27 between the point A and the point B.

According to conventional airfoil designs, the conventional meanline includes a monotonic meanline angle distribution or consistent slope sign of the meanline angle distribution (e.g., the slope angle of the meanline consistently increases or the slope angle consistently decreases), along the length of the meanline. The meanline angle is defined by the slope angle between a line that is positioned tangent to the meanline and an axial direction along the length of the meanline between end points of the meanline. In other words, in conventional airfoils, the monotonic slope angle distribution of the meanline may change consistently from a high slope value to a low slope value, or vice versa. However, in conventional airfoil designs, the slope of the meanline angle distribution does not change sign from a positive value to a negative value, or vice versa. For example, the monotonic slope angle distribution remains a consistently positive slope angle or a consistently negative slope angle along the length of the meanline between the end points of the meanline.

FIGS. 3A and 3B graphically illustrate differences between the monotonic meanline slope angle distributions and the non-monotonic meanline slope angle distributions along the length of respective meanlines for the different rotor designs. The y-axis represents angle values and the x-axis represents positions along the chord line 28, illustrated in FIG. 2, from leading edge to trailing edge. FIG. 3A illustrates the slope angle distribution along an entire length of the respective meanlines from the leading edge to the trailing edge of the airfoil near hub location. FIG. 3B illustrates the slope angle distribution along a length of the respective meanlines of the airfoil at a section near the blade tip.

As illustrated in FIG. 3A, a legend is provided for distinguishing between a baseline rotor, a rotor version 1 and a rotor version 2. The baseline rotor is identified by a dashed curve 30 that is marked by solid triangles. The baseline rotor includes a monotonic meanline angle distribution. The rotor version 1 is identified by a solid curve 34 that is marked by hollow squares. The rotor version 1 also includes a monotonic meanline angle distribution, but is distinguished from the baseline rotor meanline angle distribution by providing an improved efficiency and part speed stall margin. The rotor version 2 is identified by a dashed curve 32 that is marked by solid circles. The rotor version 2 includes a non-monotonic meanline angle distribution and further includes a meanline angle distribution that provides improved efficiency and part speed stall margin. According to one embodiment of the invention, except for variations in meanline angle distributions, all other geometrical parameters for the rotor version 1 and the rotor version 2 are the same, including the maximum thickness and the location of the airfoil shape, the leading edge thickness, the trailing edge thickness, the leading edge sweep angle and other geometrical parameters.

As illustrated by curve 30 of FIG. 3A, the baseline rotor is defined by an initial meanline angle value that decreases monotonically and linearly along the length of the meanline to a smaller meanline angle value. In other words, the meanline angle corresponding to curve 30 decreases continuously and the slope of the meanline maintains a same sign. One of ordinary skill in the art will readily appreciate that other slope distributions may be employed for the monotonic meanline angle distribution.

As illustrated by curve 34 of FIG. 3A, the rotor version 1 is defined by an initial meanline angle value that decreases monotonically and non-linearly along the length of the meanline to a smaller meanline angle value. In other words, the slope of the meanline angle corresponding to curve 34 maintains a same sign as the meanline angle value decreases. The rotor version 1 is characterized by large loading in the leading edge region, an unloaded portion in the mid-chord region and increased loading in the aft chord region. As will be described later, the meanline angle distribution of rotor version 1 introduces a double shock in the passages 11, wherein the double shock provides a lower total pressure loss than a single shock in the passages 11. The double shock and single shock in the passages 11 are provided through design of the meanline angle distribution of the rotor. As illustrated by curve 34, the concave shape in the leading edge region of the meanline angle distribution creates a droop effect that localizes the low incidence in a small area at the leading edge and maintains high efficiency (low loss), while decreasing incidence. Incidence is defined as the angle between the flow direction and the tangent line of the meanline at the leading edge. One of ordinary skill in the art will readily appreciate that other slope angle distributions may be employed for the monotonic meanline angle distribution.

As illustrated by curve 32 of FIG. 3A and curve 37 of FIG. 3B, the rotor version 2 is defined by an initial meanline angle value that decreases non-monotonically and non-linearly along the length of the meanline 27 to a smaller meanline angle value. In other words, the slope of meanline angle corresponding to curve 32 changes sign twice, at point 31 and again at point 33. As illustrated by curve 32, the leading edge region of the rotor version 2 is designed to maintain a substantially equal meanline angle distribution compared to the leading edge region of the rotor version 1. Thus, the rotor version 2 and the rotor version 1 include substantially equal stall margins at part speed. According to one embodiment, the meanline angle distribution of rotor version 2 may include a negative camber downstream of the leading edge region, which creates a gradual passage area change in passages 11 between adjacent rotor blades of versions 2, thereby removing the shock waves. Negative camber occurs when the meanline angle increases locally. One of ordinary skill in the art will readily appreciate that other slope distributions may be employed for the non-monotonic meanline angle distribution.

FIG. 3B illustrates the meanline angle distribution for a location on the meanline that is proximate to the tip of the blade. FIG. 3B provides more significant variations compared to FIG. 3A. Again, a legend is provided for distinguishing between a baseline rotor, a rotor version 1 and a rotor version 2. The baseline rotor is identified by a dashed curve 35 that is marked by solid triangles. The baseline rotor includes a monotonic meanline angle distribution. The rotor version 1 is identified by a solid curve 39 that is marked by hollow squares. The rotor version 1 also includes a monotonic meanline angle distribution, but is distinguished from the baseline rotor meanline angle distribution by providing an improved efficiency and part speed stall margin. The rotor version 2 is identified by a dashed curve 37 that is marked by solid circles. The rotor version 2 includes a non-monotonic meanline angle distribution and further includes a meanline angle distribution that provides improved efficiency and part speed stall margin. According to one embodiment of the invention, except for variations in meanline angle distributions, all other geometrical parameters for the rotor version 1 and the rotor version 2 are the same, including the maximum thickness and the location of the airfoil shape, the leading edge thickness, the trailing edge thickness, the leading edge sweep angle and other geometrical parameters.

As illustrated by curve 35 of FIG. 3B, the baseline rotor is defined by an initial meanline angle value that decreases monotonically and linearly along the length of the meanline to a smaller meanline angle value. In other words, the slope angle of the meanline angle corresponding to curve 35 maintains the same sign. The baseline rotor includes low loading at the leading edge portion of the airfoil to reduce the shock strength. One of ordinary skill in the art will readily appreciate that other slope distributions may be employed for the monotonic meanline angle distribution.

As illustrated by curve 39 of FIG. 3A, the rotor version 1 is defined by an initial meanline angle value that decreases monotonically and non-linearly along the length of the meanline to a smaller meanline angle value. The rotor version 1 is characterized by high incidence and large loading in the leading edge region and light loading in the mid-chord region to reduce shock strength. One of ordinary skill in the art will readily appreciate that other slope distributions may be employed for the monotonic meanline angle distribution.

As illustrated by curve 37 of FIG. 3B, the rotor version 2 is defined by an initial meanline angle value that decreases non-monotonically and non-linearly along the length of the meanline to a smaller meanline angle value. In other words, the slope of meanline angle corresponding to curve 32 changes sign twice, at point 36 and again at point 38 before continuing to decrease. As illustrated by curve 37, the leading edge region of the rotor version 2 is designed with a greater concave shape than the leading edge region of the rotor version 1 and has a large negative camber in the approximately 60% chord region. The rotor version 2 further includes a greater work load than the rotor version 1 in the near trailing edge region of the airfoil. One of ordinary skill in the art will readily appreciate that other slope distributions may be employed for the non-monotonic meanline angle distribution.

According to one embodiment of the invention illustrated in FIG. 4, the airfoils 13 with non-monotonic meanline slope angles improve fluid 17 flow in the passages 11 between airfoils 13. The improved fluid 17 flow in the passages 11 between airfoils 13 increases rotor efficiency. As illustrated by arrows at the inlet and egret of airfoils 13, the airfoils 13 are designed to turn the fluid 17 flow from a tangential (rotation) direction to an axial direction to achieve passage area expansion and flow diffusion. A passage meanline 41 is defined between two adjacent airfoils 13. Curves 43 a-43 d are perpendicular to the passage meanline 41 and represent cross-sectional area of the passage 11 at various locations along the passage meanline 41, between the passage inlet 45 and the passage outlet 47.

FIGS. 5A and 5B graphically illustrate differences between cross-sectional passage areas for airfoil designs that include monotonic meanline angle distributions and non-monotonic meanline angle distributions. The y-axis represents a cross-sectional area of passage 11 and the x-axis represents positions along the length of a passage meanline 41 that is defined between two adjacent airfoils 13. FIG. 5A illustrates the cross-sectional passage area variations along an entire length of the respective passage meanlines 41 between airfoils 13 near the hub of the blade. FIG. 5B illustrates the cross-sectional passage area variations along a partial length of the respective passage meanlines 41 between the airfoils 13 near the blade tip.

FIGS. 5A and 5B include a legend that distinguishes between the rotor version 1 and the rotor version 2. In FIG. 5A, the rotor version 1 is identified by a dashed curve 51, while in FIG. 5B, the rotor version 1 is identified by a dashed curve 55. As discussed above, the rotor version 1 includes a monotonic meanline angle distribution that is configured for improved efficiency and part speed stall margin. In FIG. 5A, the rotor version 2 is identified by a solid curve 53, while in FIG. 5B, the rotor version 2 is identified by a solid curve 57. The rotor version 2 includes a non-monotonic meanline angle distribution and is configured for improved efficiency and part speed stall margin. According to one embodiment of the invention, except for variations in meanline angle distributions, all other geometrical parameters for the rotor version 1 and the rotor version 2 are the same, including the maximum thickness and the location of the airfoil shape, the leading edge thickness, the trailing edge thickness, the leading edge sweep angle and other geometrical parameters.

As illustrated in FIG. 5A, the non-monotonic meanline angle distribution is positioned at the near quarter span position, thereby providing the rotor version 2 having a more uniform variation rate than the rotor version 1. As illustrated in FIG. 5B, the non-monotonic meanline angle distribution is placed at a near tip position, which reduces the cross-sectional area in the aft chord region and yields a more gradual area variation. FIGS. 5A and 5B further illustrate that, according to one embodiment, the throat is located at about 10% chord position. Since the negative camber occurs downstream of the throat in both cases, the negative camber does not affect the flow passing capacity of the passage 11.

FIG. 6A illustrates the flow angle at the passage inlet 45 and the flow angle at the passage outlet 47 along the span from the hub to tip of the blade. FIG. 6B illustrates the absolute total pressure at the passage inlet 45 and the absolute total pressure at the passage outlet 47 along the span from the hub to tip of the blade. FIGS. 6A and 6B include legends that distinguish between locations at the rotor version 1 and the rotor version 2. The leading edge of the rotor version 1 is identified by a dashed curve with a hollow square. The leading edge of the rotor version 2 is identified by a dashed curve with a hollow circle. The trailing edge of the rotor version 1 is identified by a dashed curve with a solid square. The trailing edge of the rotor version 2 is identified by a dashed curve with a solid circle.

As discussed above, the rotor version 1 includes a monotonic meanline angle distribution that is configured for improved efficiency and part speed stall margin. The rotor version 2 includes a non-monotonic meanline angle distribution and is configured for improved efficiency and part speed stall margin. According to one embodiment of the invention, except for variations in meanline angle distributions, all other geometrical parameters for the rotor version 1 and the rotor version 2 are the same, including the maximum thickness and the location of the airfoil shape, the leading edge thickness, the trailing edge thickness, the leading edge sweep angle and other geometrical parameters. As illustrated in FIGS. 6A and 6B, the airfoils having the non-monotonic meanline angle distribution provide a comparable flow turning and absolute total pressure as the airfoils having the monotonic meanline angle distribution.

FIGS. 7A and 7B illustrate an isentropic Mach number comparison between an airfoil having a monotonic meanline angle distribution and an airfoil having a non-monotonic meanline angle distribution. FIGS. 7A and 7B include legends that distinguish between the Mach number at the suction surface and the pressure surface of the airfoil for the rotor version 1 and the rotor version 2. The Mach number at the pressure surface of the rotor version 1 is identified by a solid curve with a hollow square. The Mach number at the suction surface of the rotor version 1 is identified by a solid curve with a solid square. The Mach number at the pressure surface of the rotor version 2 is identified by a dashed curve with a hollow circle. The Mach number at the suction surface of the rotor version 2 is identified by a dashed curve with a solid circle. As discussed above, the rotor version 1 includes a monotonic meanline angle distribution that is configured for improved efficiency and part speed stall margin. The rotor version 2 includes a non-monotonic meanline angle distribution and is configured for improved efficiency and part speed stall margin. According to one embodiment of the invention, except for variations in meanline angle distributions, all other geometrical parameters for the rotor version 1 and the rotor version 2 are the same, including the maximum thickness and the location of the airfoil shape, the leading edge thickness, the trailing edge thickness, the leading edge sweep angle and other geometrical parameters.

FIG. 7A illustrates the Mach number along an entire length of the blade chord 28 at a near hub location on the blade. The rotor version 1, which includes the monotonic meanline angle distribution, is defined by a Mach number at the suction surface that is identified by curve 70. Curve 70 illustrates that the suction surface of the rotor version 1 experiences a double shock at peaks 71 and 72 within the passages 11. The double shock introduces inefficiencies to the rotor and reduces the stall margin for the airfoils. The rotor version 2, which includes the non-monotonic meanline angle distribution, is defined by a Mach number at the suction surface that is identified by curve 73. Curve 73 illustrates that the suction surface of the rotor version 2 experiences a smoother single shock at peak 74 within the passages 11. The smoother single shock at peak 74 within the passages 11 is attributed to the negative camber, which provides a smooth Mach number distribution from the peak to the trailing edge. The single shock peak Mach number is substantially similar to the double shock peak Mach number. Thus, the single shock does not increase the shock strength. The single smoother shock of the rotor version 2 increases the efficiency of the rotor and improves the stall margin for the airfoils.

FIG. 7B illustrates the Mach number for a location at the near tip location on the blade. The rotor version 1, which includes the monotonic meanline angle distribution, is defined by a Mach number at the suction surface that is identified by curve 75. Curve 75 illustrates that at the near tip location, the suction surface of the rotor version 1 experiences a shock at peak 76 of over 1.3 Mach. The rotor version 2, which includes the non-monotonic meanline angle distribution, is defined by a Mach number at the suction surface that is identified by curve 77. Curve 77 illustrates that at the entry to the passage 11, the suction surface of the rotor version 2 experiences a milder shock at peak 78 of less than 1.3 Mach. Additionally, the peak shock of the rotor version 2 is moved downstream compared to the peak shock of the rotor version 1. The muted shock of the rotor version 2 increases the efficiency of the rotor and improves the stall margin for the airfoils.

FIG. 8 illustrates a comparison of a normalized efficiency from blade hub to tip between a blade having a monotonic meanline angle distribution and a blade having a non-monotonic meanline angle distribution. FIG. 8 includes a legend that distinguish between the rotor version 1 and the rotor version 2. The rotor version 1 is identified by a solid curve with a hollow square. The rotor version 2 is identified by a dashed curve with a solid square. As discussed above, the rotor version 1 includes a monotonic meanline angle distribution that is configured for maximized efficiency and part speed stall margin. The rotor version 2 includes a non-monotonic meanline angle distribution and is configured for maximized efficiency and part speed stall margin. According to one embodiment of the invention, except for variations in meanline angle distributions, all other geometrical parameters for the rotor version 1 and the rotor version 2 are the same, including the maximum thickness and the location of the airfoil shape, the leading edge thickness, the trailing edge thickness, the leading edge sweep angle and other geometrical parameters.

FIG. 8 illustrates curve 81 that represents a normalized efficiency for rotor version 1. Curve 83 represents a normalized efficiency for rotor version 2. As illustrated, the normalized efficiency for the rotor version 2 is higher across a full span of the blade, from the hub to the tip, than the efficiency for the rotor version 1. One of ordinary skill in the art will readily appreciate that other normalized efficiency curves values may be attained by varying parameters for airfoils having the monotonic meanline angle distribution and the non-monotonic meanline angle distribution.

FIGS. 9( a)-9(f) illustrate Mach number contours for a passage 11 between adjacent airfoils 13. An inlet is illustrated at a top portion and an outlet is illustrated at a bottom portion for each of FIGS. 9( a)-9(f). FIGS. 9( a), 9(c) and 9(e) illustrate Mach number contours for rotor version 1 having the monotonic meanline angle distribution. FIGS. 9( b), 9(d) and 9(f) illustrate Mach number contours for rotor version 2 having the non-monotonic meanline angle distribution.

FIGS. 9( a) and 9(b) illustrate Mach number contours at locations of near ⅓ span along the stream surface. FIGS. 9( c) and 9(d) illustrate Mach number contours at locations of near mid-span along the stream surface. FIGS. 9( e) and 9(f) illustrate Mach number contours at locations of near a tip of the span along the stream surface.

As illustrated in the contour map of FIG. 9( a), the rotor version 1 for the near ⅓ span has a strong leading edge shock in region 1 followed by a passage shock in region 2. By contrast, the contour map of FIG. 9( b) illustrates that the rotor version 2 for the ⅓ span has removed the shocks.

As illustrated in the contour map of FIG. 9( c), the rotor version 1 for the near mid-span has a strong leading edge shock in region 3 followed by a strong passage shock in region 4. By contrast, the contour map of FIG. 9( d) illustrates that the rotor version 2 has weaker shocks in corresponding region 5 and region 6. Furthermore, the shock experienced on the suction surface of region 6 impinges the airfoil at a location further downstream than the corresponding region 4 due to the weaker shock strength.

As illustrated in the contour map of FIG. 9( e), the rotor version 1 for the near tip-span has a strong leading edge shock in region 7 followed by a strong passage shock in region 8. By contrast, the contour map of FIG. 9( f) illustrates that the rotor version 2 has weaker shocks in corresponding region 9 and region 10. Furthermore, the shock experienced on the suction surface of region 10 impinges the airfoil at a location further downstream than the corresponding region 8 due to the weaker shock strength.

The foregoing is provided for purposes of illustrating, explaining, and describing embodiments of this invention. Modifications and adaptations to these embodiments will be apparent to those skilled in the art and may be made without departing from the scope or spirit of this invention. The scope of the invention is determined solely by the appended claims. 

1. A method of forming an airfoil, comprising: providing an airfoil meanline that includes a non-monotonic meanline angle distribution along a length of the airfoil meanline; and adding a thickness distribution to the airfoil meanline.
 2. The method according to claim 1, wherein the non-monotonic meanline angle distribution comprises a slope of the meanline angle distribution and includes at least one sign change along the length of the airfoil meanline.
 3. The method according to claim 2, wherein the sign of the meanline angle slope varies from a negative value to a positive value to a negative value, respectively, along the length of the airfoil meanline or from a positive value to a negative value to a positive value, respectively, along the length of the airfoil meanline.
 4. The method according to claim 1, wherein the non-monotonic meanline angle distribution includes a negative camber.
 5. The method according to claim 4, wherein the negative camber is positioned downstream of a leading edge of the airfoil.
 6. The method according to claim 4, wherein the negative camber is positioned downstream of a throat of an airfoil passage.
 7. A rotor assembly, comprising: a hub; a plurality of airfoils positioned along a perimeter of the hub and extending in a substantially radial direction, the airfoils comprising an airfoil meanline that includes a non-monotonic meanline angle distribution along a length of the airfoil meanline; and a passage defined between adjacent airfoils that receives fluid flow therebetween, wherein the passage is defined by a suction surface of a first airfoil and a pressure surface of the adjacent airfoil.
 8. The rotor assembly of claim 8, wherein the non-monotonic meanline angle distribution comprises slope values that include at least one sign change along the length of the airfoil meanline.
 9. The rotor assembly of claim 8, wherein the sign of the meanline angle slope varies from a negative value to a positive value to a negative value, respectively, along the length of the airfoil meanline.
 10. The rotor assembly of claim 8, wherein the sign of the meanline angle slope varies from a positive value to a negative value to a positive value, respectively, along the length of the airfoil meanline.
 11. The rotor assembly of claim 8, wherein the non-monotonic meanline angle distribution includes a negative camber.
 12. The rotor assembly of claim 7, wherein the negative camber is positioned downstream of a leading edge of the first airfoil.
 13. The rotor assembly of claim 7, wherein the negative camber is positioned downstream of a throat of the airfoil passage.
 14. A combustion turbine, comprising: a compressor that includes a rotor assembly located in an adverse pressure environment, the rotor assembly comprising: a hub; a plurality of airfoils positioned along a perimeter of the hub and extending in a substantially radial direction; and a passage defined between adjacent airfoils that receives fluid flow therebetween, wherein the passage is defined by a suction surface of a first airfoil and a pressure surface of the adjacent airfoil, wherein the suction surface of the first airfoil includes a negative camber; a combustor coupled to the compressor; and a turbine coupled to the combustor.
 15. The combustion turbine of claim 14, wherein the plurality of airfoils include an airfoil meanline having a non-monotonic meanline angle distribution along a length of the airfoil meanline.
 16. The combustion turbine of claim 15, wherein the non-monotonic meanline angle distribution comprises angle values that include at least one sign change along the length of the airfoil meanline.
 17. The combustion turbine of claim 16, wherein the sign of the meanline angle slope varies from a negative value to a positive value to a negative value, respectively, along the length of the airfoil meanline or from a positive value to a negative value to a positive value, respectively, along the length of the airfoil meanline.
 18. The combustion turbine of claim 15, wherein the non-monotonic meanline angle distribution includes a negative camber.
 19. The combustion turbine of claim 14, wherein the negative camber is positioned downstream of a leading edge of the first airfoil.
 20. The combustion turbine of claim 14, wherein the negative camber is positioned downstream of a throat of an airfoil passage. 